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The mass and diameter of a planet are twice that of the earth. What will be the time period of oscillation of a pendulum on this planet, if it is a seconds pendulum on earth

a
2  seconds
b
2 seconds
c
12  seconds
d
22  seconds

detailed solution

Correct option is D

acceleration due to gravity on Earth is ge=GMR2 acceleration due to gravity on planet is gp=GMpRp2 Given radius of planet Rp=2Rearth=2Re given mass of planet Mp=2Mearth=2Megpge=GMpRp2×Re2GMe substitute values of Rp=2RE,MP=2Me gpge=2Re24Re2=12 gp=ge2  ........(1) TeTp=gpge=ge/2g=12 substitute time period on earth =2 that of seconds pendulum 2Tp=12⇒Tp=22  seconds.

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A simple pendulum has time period T1. The point of suspension is now moved upward according to equation y=kt2  where k=1m/sec2. If new time period is T2 then ratio T12T22  will be


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